Subspace Corrections Method and Its Applications to the Construction and the Convergence Analysis of Multilevel Methods

报告摘要：

In this talk we present results related to the convergence of multilevel/multigrid methods, applied to discretizations of elliptic PDEs, that lead to symmetric positive definite linear systems. The presentation is based on the subspace correction framework. The abstract theory is applied to examples coming from finite element discretizations of scalar elliptic partial differential equations and we show how some of the known estimates of the convergence rate of the multigrid method can be obtained in a straightforward fashion. We also comment on some special two level techniques that are used in construction of optimal Algebraic Multigrid Methods.